Author | Morandi, Patrick. author |
---|---|
Title | Field and Galois Theory [electronic resource] / by Patrick Morandi |
Imprint | New York, NY : Springer New York, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4040-2 |
Descript | XVI, 284 p. online resource |
I Galois Theory -- 1 Field Extensions -- 2 Automorphisms -- 3 Normal Extensions -- 4 Separable and Inseparable Extensions -- 5 The Fundamental Theorem of Galois Theory -- II Some Galois Extensions -- 6 Finite Fields -- 7 Cyclotomic Extensions -- 8 Norms and Traces -- 9 Cyclic Extensions -- 10 Hubert Theorem 90 and Group Cohomology -- 11 Kummer Extensions -- III Applications of Galois Theory -- 12 Discriminants -- 13 Polynomials of Degree 3 and 4 -- 14 The Transcendence of ? and e -- 15 Ruler and Compass Constructions -- 16 Solvability by Radicals -- IV Infinite Algebraic Extensions -- 17 Infinite Galois Extensions -- 18 Some Infinite Galois Extensions -- V Transcendental Extensions -- 19 Transcendence Bases -- 20 Linear Disjointness -- 21 Algebraic Varieties -- 22 Algebraic Function Fields -- 23 Derivations and Differentials -- Appendix A Ring Theory -- 1 Prime and Maximal Ideals -- 2 Unique Factorization Domains -- 3 Polynomials over a Field -- 4 Factorization in Polynomial Rings -- 5 Irreducibility Tests -- Appendix B Set Theory -- 1 Zornโs Lemma -- 2 Cardinality and Cardinal Arithmetic -- Appendix C Group Theory -- 1 Fundamentals of Finite Groups -- 2 The Sylow Theorems -- 3 Solvable Groups -- 4 Profinite Groups -- Appendix D Vector Spaces -- 1 Bases and Dimension -- 2 Linear Transformations -- 3 Systems of Linear Equations and Determinants -- 4 Tensor Products -- Appendix E Topology -- 1 Topological Spaces -- 2 Topological Properties -- References